$f(x) = -3x$ $g(n) = -7n^{2}+5(f(n))$ $ f(g(-2)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-2)$ . Then we'll know what to plug into the outer function. $g(-2) = -7(-2)^{2}+5(f(-2))$ To solve for the value of $g$ , we need to solve for the value of $f(-2)$ $f(-2) = (-3)(-2)$ $f(-2) = 6$ That means $g(-2) = -7(-2)^{2}+(5)(6)$ $g(-2) = 2$ Now we know that $g(-2) = 2$ . Let's solve for $f(g(-2))$ , which is $f(2)$ $f(2) = (-3)(2)$ $f(2) = -6$